Spectral correspondence for cyclic Higgs bundles
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914562379350016 |
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| author | Lee, Jia Choon Peón-Nieto, Ana |
| author_facet | Lee, Jia Choon Peón-Nieto, Ana |
| contents | In this paper, we describe the spectral correspondence for cyclic Higgs bundles from the viewpoint of quiver bundles. Under this framework, we establish a one-to-one correspondence between cyclic Higgs bundles on a curve and sheaves on a noncommutative surface whose noncommutative structure originates from the path algebra associated to the cyclic quiver. As applications, this correspondence generalizes the known spectral correspondence for $U(p,p)$-Higgs bundles and establish a connection between the spectral data for $U(p,q)$-Higgs bundles and modules over the sheaf of even Clifford algebras of a conic fibration. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03249 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Spectral correspondence for cyclic Higgs bundles Lee, Jia Choon Peón-Nieto, Ana Algebraic Geometry In this paper, we describe the spectral correspondence for cyclic Higgs bundles from the viewpoint of quiver bundles. Under this framework, we establish a one-to-one correspondence between cyclic Higgs bundles on a curve and sheaves on a noncommutative surface whose noncommutative structure originates from the path algebra associated to the cyclic quiver. As applications, this correspondence generalizes the known spectral correspondence for $U(p,p)$-Higgs bundles and establish a connection between the spectral data for $U(p,q)$-Higgs bundles and modules over the sheaf of even Clifford algebras of a conic fibration. |
| title | Spectral correspondence for cyclic Higgs bundles |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2605.03249 |